If society actively encouraged the creation of more positive ways to contribute positive things, I bet we'd see an "organic" growth in numbers of people choosing to do so.
Example; There've been some pretty positive things happening around community gardens in some places (when they're not being attacked by self-appointed neighborhood Nannies that don't like to see people gathering together around something beneficial).
Example 2; I remember "maker" clubs and similar community groups doin' lots of really fun activities that benefited more than just the group itself (free community virus cleanups, operating system install parties, community LAN parties - everyone's welcome).
I'm sure that if enough positive activities were presented to society as a whole, you'd just naturally find a growing percentage of humanity doin' good things for each other that used to be considered "work" at some point in the past before whatever "safety net" made it unnecessary to do for survival's sake anymore. People might even still do some of those things at a higher level of quality than others and net themselves some personal gain out of it.
Problem is that humans aren't willing to cooperate with one another enough to even approach any sort of Utopian ideal, and they're often too ready to jump at all the reasons such a thing is "impossible" without being willing to even consider any ideas that might lead to it bein' a reality.